This work explores the potential of the proposed FASER2 experiment at the LHC to determine the properties of a discovered heavy neutral lepton (HNL), including its mass, couplings, and whether it is a Majorana or Dirac fermion. We first consider a Majorana HNL with mass m_N = 1.84 GeV that is primarily produced through decays D → μN at the ATLAS interaction point. Such HNLs may travel macroscopic distances in the far-forward direction and then decay, yielding approximately 8600 N → μπ decays in FASER2 at the High-Luminosity LHC. With FASER2 measurements alone, the HNL's mass and couplings can be measured to fractional uncertainties of approximately 0.1% and 3% at 95% CL, respectively, and the Dirac fermion hypothesis can be rejected at 99.8% CL. We then consider a second, more difficult, case of a Majorana HNL with mass m_N = 2.00 GeV, yielding only 80 N → μπ decays in FASER2. With FASER2 alone, measurements of HNL properties are still possible, but somewhat less precise. However, by using FASER2 as a trigger for ATLAS and measuring the charge of the muon produced in association with the HNL at ATLAS to search for lepton number violation, one can precisely measure the HNL's properties and reject the Dirac fermion hypothesis at 99.7% CL. These results show that FASER2, sometimes in coordination with ATLAS, can precisely determine HNL properties, with far-reaching implications for our understanding of neutrino masses, baryogenesis, and the fundamental symmetries of nature.

Heavy neutral leptons (HNLs) are motivated by attempts to explain neutrino masses and dark matter. If their masses are in the MeV to several GeV range, HNLs are light enough to be copiously produced at collider and accelerator facilities, but also heavy enough to decay to visible particles on length scales that can be observed in particle detectors. Previous studies evaluating the sensitivities of experiments have often focused on simple, but not particularly well-motivated, models in which the HNL mixes with only one active neutrino flavor. In this work, we accurately simulate models for HNL masses between 100 MeV and 10 GeV and arbitrary couplings to e, μ, and τ leptons. We include over 150 HNL production channels and over 100 HNL decay modes, including all of the processes that can be dominant in some region of the general parameter space. The result is HNLCalc, a user-friendly, fast, and flexible library to compute the properties of HNL models. As examples, we implement HNLCalc to extend the FORESEE package to evaluate the prospects for HNL discovery at forward LHC experiments. We present sensitivity reaches for FASER and FASER2 in five benchmark scenarios with coupling ratios |U_e|² : |U_μ|² : |U_τ|² = 1:0:0, 0:1:0, 0:0:1, 0:1:1, and 1:1:1, where the latter two have not been studied previously. Comparing these to current constraints, we identify regions of parameter space with significant discovery prospects.